September 11 conspiracy theorists claim that the Pentagon was hit by a missile rather than a plane. Photograph: PA

Barbara Olson is dead, that much is certain.

But did the conservative television commentator meet her end on board American Airlines flight 77 as it crashed into the Pentagon, just minutes after Olson made last, desperate phone calls to her husband, the US solicitor general?

Or was Olson secretly abducted, the phone calls faked using voice morphing technology and her body dumped at sea after the Pentagon was really struck by a missile as part of a government plot to fabricate the September 11 attacks?

As preposterous as the claim that the real September 11 conspiracy was not an al-Qaida plot but some convoluted Washington intrigue may appear, there are large numbers of people who believe it.

The September 11 attacks have spawned bestselling books, popular films and an indeterminate number of conspiracy websites run by "truthers" whose theories revolve around plots far more complex than that perpetrated by al-Qaida.

Among the most pervasive is that the twin towers of the World Trade Centre were brought down by controlled explosions; that the Israeli intelligence service knew the attacks were coming because, it is wrongly claimed, no Jews died; and that the planes that hit the towers were packed with explosive and flown by remote control.

Not since President John F Kennedy was felled by bullets in Dallas nearly half a century ago have conspiracy theorists had so much to get their teeth into although, tellingly, a number of those who see a government plot on September 11 can also be found claiming that the Holocaust is a myth.

But that does not mean they are not taken seriously. According to one poll, by 2006 one in three Americans believed that the Bush administration had a hand in the 9/11 attacks, either in intentionally letting them go ahead in order to justify invading Iraq, or in carrying them out.

The US government grew so concerned that in 2009 it issued a document attempting to debunk the conspiracy theories. It has not worked.

Robbyn Swan, co-author of a recently released book on the attacks – The Eleventh Day: The Full Story of 9/11 and Osama bin Laden, which examines the origins of the conspiracy theories – said doubts that planes brought down the twin towers were first raised on the day of the attack.

"They sprang up earlier than people realised. A chap by the name of David Rostcheck, perfectly innocently, just watching the twin towers fall, got on the internet to a chatroom early in the afternoon of September 11 and said: 'It looks like a controlled demolition and if we don't hear more about that in the next few days then there's something really wrong.' "

"That idea took hold," said Swan. "The theories come from everywhere and all of it spurred on by this creature, the internet, which had not existed before. In the 1960s, when the Kennedy assassination conspiracy theories were heating up, there was no way to spread them except by letter which was the equivalent of using the pony express compared to the way information passes now."

Among those who see a government conspiracy are CIA veterans, former soldiers and academics.

David Griffin, a professor of theology, has written nine books purporting to prove that the September 11 attacks were "masterminded from inside the American state apparatus" in order to justify imperial adventures in the Middle East. That's a theory that strikes a chord in the Arab world in particular, in large part to shift responsibility from Muslim extremists. That inevitably leads some to blame Israel.

Griffin is also one of those who says that the calls made by the terrified doomed passengers on the hijacked planes were faked using "voice morphing technology" because their mobile phones would not have worked at altitude. Except phone records show that the calls made by Olson and others were from phones fitted into the back of aircraft seats.

Steven Jones, a physicist, was relieved of his teaching duties at Brigham Young University after claiming to have built a body of scientific evidence that the twin towers were brought down by controlled explosions as part of a US government plot. His claims are based on his analysis of what he says were dust and rubble samples from the scene, although critics have pointed out that the samples were posted to Jones years after the event by people who said they collected them on 9/11, but for which there is no corroboration.

In the US, a series of films called Loose Change 9/11: An American Coup questioned whether a plane crashed into the Pentagon, what caused the World Trade Centre towers to collapse and disputed accounts that passengers made phone calls from doomed planes. It has sold more than a million copies on DVD and been shown on Fox television local channels.

A French author, Thierry Meyssan, had a bestseller – 9/11: The Big Lie – within months of the attacks by claiming the Pentagon was destroyed by a missile and aircraft parts were brought to the scene to fake the crash.

It is a theory supported by Dean Hartwell who claims in his books – Planes without Passengers: the Faked Hijackings of 9/11 and Osama bin Laden Had Nothing to Do with 9/11 – to have uncovered documentary evidence that two of the hijacked flights never took off and the other two landed safely in secret.

So what happened to Olson and the others who died on those aircraft?

"The people who got on the planes were simply pawns. They were, whether wittingly or unwittingly, directed to show up at the airport terminal just to show people who were watching that there were passengers. They were simply agents and they were given new identities," he said. "The government wanted to fake plane attacks to scare the public. We saw horrible images on television that were designed to provoke us into supporting wars in Afghanistan and Iraq."

Swan says that given the scale of such a conspiracy within the US system – which would have involved not only the military and FBI but airlines and rescue workers – it is hard to imagine that in 10 years no one has revealed their part. Hartwell is not deterred.

"If someone were to come forward and say they were on the inside I'm not sure who would believe them. They may have been told they were part of a simulation. I don't think they were told the whole story. They may well have been paid or threatened to keep quiet," he said.

To Swan, the theories would be laughable if they were not, as she puts it in her book, "cruel insults to the memory of the dead" such as Olson who was one of 64 people killed on Flight 77.

"I invite anyone who believes that to talk to the many eyewitnesses who saw the plane approach and hit the Pentagon," said Swan. "I invite them to look, as I have done, at the absolutely horrific photographs of the burned bodies of the victims of flight 77 still strapped into their plane seats that were found amongst the ruins of the Pentagon."

Hartwell insists that all such evidence was fabricated on the orders of the White House and Pentagon. But if he had indeed stumbled on the truth, surely those running a conspiracy of such magnitude would seek to silence him, perhaps even kill him, too?

"It would be quite suspicious if anything were to happen to me at this time. It would prove I was right," he said.